Sandy Hook Elementary adopted a new safety plan this year, and even conducted drills. Principal Dawn Hochsprung tweeted a picture of one of those drills in October with the caption, "Safety first at Sandy Hook." But those measures didn't prevent the killings.

Joseph Cirasuolo, Executive Director of the Connecticut Association of Public School Superintendents, spoke to Rebecca Jarvis and Anthony Mason on "CBS This Morning: Saturday" and said no amount of security alone will prevent another gun massacre.

"Security's going to get beefed up at every school in the country, I'm sure," he said. "But that's no guarantee that this kind of thing can't happen again until we deal with the fact that people who are disturbed are getting their hands on guns, and you can see what happens when that happens."

Cirasuolo said the school building will remain closed for a while, but the local superintendent is trying to get the students back into other schools before Christmas.

"She's going to have to make some arrangements," he said. "A number of the school districts in the area are offering space, if needed."

Cirasuolo also said grief and trauma counseling will be offered for the students.

To watch the full interview with Joseph Cirasuolo, click on the video player above.